Math 540 Fall 2025

Introduction to algebraic topology

This is a standard first course in algebraic topology.  We will cover the following topics:  fundamental group and covering spaces, singular, simplicial, and cellular homology.  Along the way, we will introduce many interesting examples from differential topology, Lie groups, and prove some nice applications (including Brouwer's fixed point theorem, Jordan-Brouwer theorem, and persistent homology for topological data analysis). I will also adjust the content of the course according to your interests.

There will be no midterms and final exams.  Homework will be assigned weekly and will be graded.  The final grade of the course depends on the homework grades.

Text:

Allen Hatcher, Algebraic Topology

Prerequisites:

Point-set topology and abstract algebra (groups, rings, fields).

 

If you have any questions, please let me know by email: fluo@math.rutgers.edu.